A Hilbert Lemniscate Theorem in \mathbb{C}^2

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

Hilbert ’ S Theorem

In modern form, Hilbert’s Theorem 90 tells us that Rǫ∗(Gm) = 0, where ǫ : Xét → Xzar is the canonical map between the étale site and the Zariski site of a scheme X. I construct examples showing that the corresponding statement for algebraic spaces does not hold.

Quantitative Forms of a Theorem of Hilbert

Lemniscate growth

It was recently noticed that lemniscates do not survive Laplacian growth [12] (2010). This raises the question: “Is there a growth process for which polynomial lemniscates are solutions?” The answer is “yes”, and the law governing the boundary velocity is reciprocal to that of Laplacian growth. Viewing lemniscates as solutions to a moving-boundary problem gives a new perspective on results from...

A Representation Theorem for Schauder Bases in Hilbert Space

A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...